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Question 639838: find the perimeter of triangle ABC. A=(1,4, B=(-2,-1)C=(-3,-2)
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The perimeter of triangle ABC is the sum of the distances AB, BC, and CA, the distances between the points.
Your book and/or your teacher may have given you a formula for distance between two points that looks complicated. Different teachers an/or different books will write it differently, but all the different versions mean the same thing. If your teacher expects you to write it out, write it the way it was written in your class. The important part is understanding what the formula does (and maybe why), and being able to apply it without getting all mixed up.
The formula is based on the Pythagorean theorem.
It uses the x-coordinates and y-coordinates of the points.
The difference in x-coordinates and the difference in y-coordinates are calculated first. Disregarding any posnegative signs, thoase are the lengths of the horizontal and vertical legs of a right triangle.
I drew those legs in green for points A and B.
To calculate the distance between the two points (length of the hypotenuse),
the squares of the differences in coordinates are calculated, and added up.
Then the square root of that sum is calculated.
For points A and B.
The difference in x-coordinates is  .
The difference in y-coordinates is  .
Those difference are squared and added to get
Then the square root is calculated to find the distance AB:
All in one step:
Similarly,
Adding it all up,
I do not see any nicer-looking way to write it.
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